title: Modeling of experts' divergent prior beliefs for a sequential phase III clinical trial.
abstract: BACKGROUND
  There have been few Bayesian analyses of phase III sequential clinical trials that model divergent expert opinions in a single distribution.
  
  
  OBJECTIVE
  We used modeling of experts' opinions to perform additional Bayesian analyses of a randomized clinical trial (designed as a sequential trial), particularly when a bimodal shape is observed. We provide an illustrative example based on a randomized trial conducted in patients aged between 65 and 75 years with multiple myeloma as the case study.
  
  
  METHODS
  The main endpoint of the trial was overall survival (OS). Prior distribution of the log hazard ratio of death in the experimental versus the control arm ( $$\theta $$ ) was constructed based on elicitation of experts using a mixture of normal distributions estimated by the Expectation-Maximisation (EM) algorithm. At each interim and terminal analysis, the posterior probability of $$\theta $$ and the resulting increases in median OS in the experimental arm compared to the control were computed. The results were compared to results obtained using either skeptical, enthusiastic, or a mixture of those priors. Finally, we discuss our results in light of the frequentist approach originally designed for the trial.
  
  
  RESULTS
  A total of 39 experts reported their opinion on the median OS in the experimental arm compared to the median control survival of 30 months. The resulting pooled distribution of the log hazard ratios exhibited a bimodal profile. When the prior mixture of the normal distribution was fitted to the data sets from the experts, 44% of the experts' opinions were optimistic and 56% were doubtful. At the final analysis, the percentage of doubting experts dropped to 18%. This corresponded to a posterior probability of an improved OS in the experimental arm compared to the control arm of at least 0.98, regardless of the prior. These findings are in agreement with the original conclusion of the trial regarding the beneficial effect of the experimental treatment in this population.
  
  
  CONCLUSIONS
  Only 39 experts among the 120 questioned physicians responded to the inquiry. Our approach was hybrid because the prior mixture was estimated using the EM algorithm, and a full Bayesian approach may have been used.
  
  
  CONCLUSIONS
  Bayesian inference allows the quantification of increased survival in terms of probability distributions and provides investigators with an additional tool in the analysis of a randomized phase III clinical trial. Using a mixture of densities appears to be a promising strategy for incorporating the bimodal profile of prior opinion, with actualization of the two components along the trial as an illustration of the evolution of opinions as data are accumulated.
authors.affiliation: INSERM UMR-717, Biostatistics and Clinical Epidemiology Research Unit, Université Paris Diderot - Paris 7, Paris, France. marion.moatti@univ-paris-diderot.fr
authors.forename: Marion
authors.initials: M
authors.lastname: Moatti
authors.forename: Sarah
authors.initials: S
authors.lastname: Zohar
authors.forename: Thierry
authors.initials: T
authors.lastname: Facon
authors.forename: Philippe
authors.initials: P
authors.lastname: Moreau
authors.forename: Jean-Yves
authors.initials: JY
authors.lastname: Mary
authors.forename: Sylvie
authors.initials: S
authors.lastname: Chevret
mesh_terms: D000368:Aged; D020533:Angiogenesis Inhibitors / Q000627:therapeutic use; D018931:Antineoplastic Agents, Hormonal / Q000627:therapeutic use; D001499:Bayes Theorem; D004359:Drug Therapy, Combination; D006801:Humans; D008558:Melphalan / Q000627:therapeutic use; D015233:Models, Statistical; D009101:Multiple Myeloma / Q000188:drug therapy / Q000401:mortality*; D019653:Myeloablative Agonists / Q000627:therapeutic use; D011241:Prednisone / Q000627:therapeutic use; D033581:Stem Cell Transplantation; D011795:Surveys and Questionnaires; D016019:Survival Analysis; D013792:Thalidomide / Q000627:therapeutic use
chemical_list: D020533:Angiogenesis Inhibitors; D018931:Antineoplastic Agents, Hormonal; D019653:Myeloablative Agonists; D013792:Thalidomide; D008558:Melphalan; D011241:Prednisone